Do EEVEE samples have any effect when rendering?
There are several things affected by EEVEE sampling, as you can see in this example scene, rendered at 1, 8 and 64 samples:


soft shadows are obtained by sampling large light sources using many small light sources. Low samples will &quot;reveal&quot; the point lights. This is generally the main downside of a low-sample rendering, therefore you should choose the number of samples based on how good your soft shadows look.
 top view: 

the direction of refracted and reflected is also sampled because, especially around the corners, a sub-pixel change in the direction of the ray can make a difference between hitting an object, another object, or the sky. For low samples, this results in a strange pixelated blur


aliasing is what happens when a curved profile is drawn using pixels: it gets jagged if the pixels aren't &quot;smoothed&quot; (antialiased) adequately. More samples make the contours smoother.


[Added Sept 2020] the quality of Alpha Hashed transparency is also affected by the global sampling. Indeed, for each sample, a pixel will either be rendered as fully opaque or fully transparent: a fractional transparency is a result of averaging over multiple samples. With too few samples, tranparency appears patched/noisy:


[Added Sept 2020, suggested by Andrey Sokolov] the number of volumetric slices rendered depends on the EEVEE sampling: note how at 1 sample the dust cloud appears 2-dimensional.
PS There is another &quot;Samples&quot; count inside the Volumetric tab that controls the quality of each slice, and is independent of the global EEVEE sampling.